标题： 具有宇宙项的$2+1$维时空中的引力解耦 显示英文标题

标题： Gravitational decoupling in $2+1$ dimensional space--times with cosmological term

摘要： 在这项工作中，我们实现了最小几何变形方法，以获得具有宇宙常数的任意各向异性爱因斯坦场方程解在$2+1$维时空中的各向同性部分和解耦物质内容。 我们得到，这两个扇区的解可以解析地用原始各向异性解的度规函数来表示，而不是像其$3+1$对应版本中的形式积分。 作为一个特定的例子，我们研究了一个正则黑洞解，并表明根据宇宙常数的符号，这些解对应于违反零能条件的正则黑洞或没有奇异毛发的非正则黑洞。 讨论了奇异/非奇异与正则/非正则黑洞之间的对偶性。 显示英文摘要

摘要： In this work we implement the Minimal Geometric Deformation method to obtain the isotropic sector and the decoupler matter content of any anisotropic solution of the Einstein field equations with cosmological constant in $2+1$ dimensional space--times. We obtain that the solutions of both sectors can be expressed analytically in terms of the metric functions of the original anisotropic solutions instead of formal integral as in its $3+1$ counterpart. As a particular example we study a regular black hole solution and we show that, depending on the sign of the cosmological constant, the solutions correspond to regular black holes violating the null energy condition or to a non--regular black hole without exotic hair. The exotic/non--exotic and the regular/non--regular black hole dualities are discussed.